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| Fig. 1: Example of a tidal energy turbine. (Source: Wikimedia Commons) |
Tides are the regular rise and fall of sea level caused by the gravitational pull of the Moon and, to a lesser extent, the Sun. The Moon pulls slightly more strongly on the side of Earth closest to it and slightly less on the far side, creating two tidal bulges. As Earth rotates through these bulges, coastal regions experience alternating high tide and low tide, with high and low tidal heights respectively. Because the Moon moves in its orbit while Earth rotates, the tidal cycle is not exactly 12 hours but about 12 hours and 25 minutes. These slow, planetary-scale changes in sea level move enormous volumes of water, producing strong tidal currents. This begs the questions: how much energy do the tides generate, and can we harness that energy?
Let's put an upper bound on the possible power we can harness from the tides, by first placing an upper bound on how much power they generate. We can do so using the rate at which the earth's rotation is slowing down (this effect is primarily due to the tides, which then dissipate the energy mostly as heat). Not all the power lost to tidal drag goes into the oceans, so we note that this calculation merely places an absolute upper bound on the possible energy one can harvest from the tides. From studies analyzing coral bands (the annual growth layers in coral skeletons), it is measured that the earth's rotation time is increasing by roughly 1.5ms per century. [1,2]
We can express the energy of the earth's rotation as
| E | = | (1/2) I ω2 |
where ω is the angular velocity of the earth, and I is the moment of inertia. Taking the derivative of either side of this equation yields
| dE/dt | = | I ω (dω/dt) |
Here dE/dt is the change in the earth's rotational energy per unit time, which has the same magnitude as the power generated by the tides. Below we use T, which is earth's rotational period in seconds, and we take earth's moment of inertia from Chambat and Valette. [3] Specifically, the earth's moment of inertia is calculated via satellite-measured gravity field coefficients. Calculating each term, we obtain
| I | = | 8.04 × 1037 kg m2 | ||
| ω | = | 2π/T = 2π/(86400 sec) = 7.27 × 10-5 sec-1 | ||
| dω/dt | = | (- 2π /T2)(dT/dt) | ||
| = | - 2π (86400 sec)2 |
× | 1.5 × 10-3 sec
century-1 100 year century-1 × 365 d year-1 × 86400 sec d-1 |
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| = | - 4.0 × 10-22 sec-2 | |||
Putting this all together yields
| - dE/dt | = | 8.04 × 1037 kg m2 × 7.27 × 10-5 sec-1 × 4.0 × 10-22 sec-2 |
| = | 2.3 × 1012 Watts |
or 2.3 terawatts. Since this is the rate at which energy is being stripped from the earth's rotation. This is the power of the tides. We can compare this with the global average power budget, which is roughly 18 terawatts. [4] This means that even if we could harness the total energy of the tides (or in other words, stop the tidal flow), the energy is only a fraction of the world's power budget. We can contrast this with solar energy, where we would only need to cover 0.3% of the earth's surface to supply the world's electricity. [5]
Despite the small total energy of tidal power with respect to the world's budget and other renewable energy sources, efforts are being made to harness tidal power, using tidal energy turbines (an example of which is shown in Fig. 1). [6] For example, the Sihwa Lake Tidal Power Station in South Korea represents a modern, large-scale implementation of tidal-range power generation. Constructed on an existing seawall originally built for flood control, the facility employs ten bulb-type turbines with a combined installed capacity of 254 MW, making it the largest tidal power plant currently in operation. [7] The plant operates using a single-effect flood-generation scheme, exploiting the substantial tidal range of the Yellow Sea to produce electricity in a highly predictable manner. Engineering and performance analyses estimate that Sihwa Lake generates approximately 553 GWh of electricity annually, illustrating the capability of tidal-barrage systems to deliver consistent, utility-scale renewable energy over long operational lifetimes. [7]
© Pranav Kakhandiki. The author warrants that the work is the author's own and that Stanford University provided no input other than typesetting and referencing guidelines. The author grants permission to copy, distribute and display this work in unaltered form, with attribution to the author, for noncommercial purposes only. All other rights, including commercial rights, are reserved to the author.
[1] G. B. Arfken, International Edition University Physics (Academic Press, 2012), pp. 212-228.
[2] B. Canrtrall, "Tidal Energy as a Renewable Energy Source," Physics 240, Stanford University, Fall 2023.
[3] F. Chambat and B. Valette, "Mean Radius, Mass, and Inertia For Reference Earth Models," Phys. Earth Planet. Inter. 1224, 237 (2001).
[4] "BP Statistical Review of World Energy 2022," British Petroleum, June 2022
[5] M. Victoria et al., "Solar Photovoltaics Is Ready to Power a Sustainable Future," Joule 5, 1041 (2021).
[6] C. Shetty and A. Priyam, "A Review on Tidal Energy Technologies," Mater. Today Proc. 86, 2774 (2022).
[7] Y. H. Bae, K. O. Kim, and B. H. Choi, "Lake Sihwa Tidal Power Plant Project," Ocean Eng. 17, 454 (2010).
